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Materials
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Potions:
6 Strenght II (awkward + blaze powder + redstone)
12 Instant Healing II (need 2 glistening melons from potato guy and 2 glowstone dust)
6 Night Vision Extended (awkward + 2 golden carrot from potato guy + 2 redstone. The wither can get in dark places so it's better to make sure you can always see him)
6 Fire Resistance Extended (optional, 2 magma cream + 2 redstone, only for the case the wither finds some lava and stay there)
3 Leaping (very optional, if you have 1 rabbit foot, for the case the wither destroys so much blocks it's hard to go after him, this is very rare)

Food:
Golden Apples (about 8 or as many as you can, some farmers sell apples, but I don't remember if potato guy sells)
Golden Carrots (about 12? potato guy sell them)

Armor with Protection IV or maybe Blast Protection IV (you can't have both in the same piece and you already have Protection IV which is better for dragon and wither skeleton, but Blast Protection is better for wither, so maybe try making a piece or two with Blast Protection with the diamonds you saved after getting the skulls)

Weapons
Smite V Sword
Power V Bow (and arrows, only 1 is enough if you have Infinity)

1 Pickaxe (any will do)
1 shovel (any will do)
64 Torches
3 Milk Buckets

4 soul sand
3 wither skulls

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Tactic
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1. Go Underground to level 5 anywhere far from your base. Around your base there are too many tunnels already we want an area with only the tunnels you will make just for the fight.

2. Make a 100 blocks long tunnel, 1 wide, 2 high.

3. At the end of this tunnel make a chamber to summon the wither. It should be around 5 x 5 and 4 high.

4. Continue the tunnel after the chamber, more 100 blocks. So now you have two tunnels meeting in the chamber. You will probably need only one tunnel, the other is for safety.

5. Go to the chamber, place the soul sand and wither skulls to summon the wither. Run to any of the tunnels. Wait for the wither to explode from a safe distance, at least 20 blocks.

6. Drink a Night Vision potion

7. After the explosion look where it is and carefully go after him with your bow. He will be slowly destroying the blocks to go after you or a mob in a nearby cave if you are lucky. Shoot him with the bow till he has only half health. Use Instant health and golden apples when needed. In last case if the wither effect is killing you drink milk to erase all effects.

8. When he is at half health drink a strength potion and go for him in melee combat, just go to him and hit him with your sword. He will wither you, ignore that and keep hitting, critical hits (jump and hit when falling) is better. You should kill him before he kills you. When he is dead drink the milk or you will die too.

That's what I have to suggest. You are doing a great job. Good luck.